CN109284478A - A method of estimation lognormal type unit dependability parameter - Google Patents
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Abstract
The invention discloses a kind of methods for estimating lognormal type unit dependability parameter, the following steps are included: step 1: determining candidate service life distribution parameter, according to existing lognormal type unit reliability data, cell life logarithmic average parameter lower limit value μ to be estimated is determinedminWith upper limit value μmaxAnd service life logarithm standard deviation parameter lower limit value σminWith upper limit value σmax, and logarithmic average parameter step length d1 and logarithm standard deviation parameter step length d2 is determined according to upper lower limit value respectively, calculate μ 1j1With σ 1j2, then to μ 1j1With σ 1j2Carry out traversal combination；Step 2: traversal service life logarithmic average parameter μjWith logarithm standard deviation parameter σjCombination calculate likelihood value.It finds maximum likelihood value and is denoted as LM, then maximum likelihood value LMCorresponding μMFor the estimated value of service life logarithmic average parameter, σMFor the estimated value of service life logarithm standard deviation parameter.The present invention utilizes " a small amount of reliability test data+in product development, production, the mass data for the stages such as using to generate ", estimates the regularity of distribution of life of product.
Description
Technical field
The invention belongs to reliability test technical field, in particular to a kind of life expectancy obeys the distribution of lognormal type
The method of unit dependability parameter.
Background technique
Reliability is to describe the core attribute of product quality, usually uses the regularity of distribution (distribution pattern and parameter) in service life
Carry out quantitative description reliability.Theoretically, carry out a large amount of reliability test for product, sufficient amount of product can be obtained
Then mature mathematical statistics method can be used to estimate the distribution pattern and parameter of life of product in lifetime data.But in reality
In the work of border, carry out a large amount of reliability tests for product, often means that high economic cost and very long test consumption
When, therefore more common way is to utilize that " a small amount of reliability test data+in product development, production such as uses to produce at the stages
Raw mass data " estimates the regularity of distribution of life of product.In the reliability test of product, generally be equipped with it is special
Line detection device for the integrity state of real-time monitoring product, the fault moment of timely record product, therefore can obtain
The numerical value of life of product.But in the case where product development, production, these non-reliability test scenes such as using, not necessarily equipped with special
The online detection instrument of door periodically or non-periodically can only carry out integrity inspection to product, thus cannot accurately know product
Fault moment, also can not just obtain the numerical information in service life.
Summary of the invention
In order to overcome defect present in background technique, the present invention provides a kind of estimation lognormal type unit reliability
The method of parameter
To achieve the goals above, a kind of the technical solution adopted by the present invention are as follows: estimation lognormal type unit reliability
The method of parameter, comprising the following steps:
Step 1: candidate service life distribution parameter is determined, according to the distribution of existing lognormal type unit reliability data
Rule primarily determines the service life logarithmic average parameter lower limit value μ of logarithm normal distribution unit to be estimatedminIn logarithmic average parameter
Limit value μmaxAnd the logarithm standard deviation parameter lower limit value σ of logarithm normal distribution to be estimatedminWith logarithm standard deviation parameter upper limit value σmax；
In the service life logarithmic average parameter section of determining logarithm normal distribution unit, n1 candidate is generated at equal intervals
The logarithmic average parameter of logarithm normal distribution, in candidate parameter, the equal step-length of adjacent logarithmic average parameter is d1, according to right
The step-length of number Mean Parameters successively calculates the logarithmic average parameter μ 1 of n1 logarithm normal distributionj1, wherein 1≤j1≤n1；
In the service life logarithm standard deviation parameter section of determining logarithm normal distribution unit, n2 time is generated at equal intervals
Select the logarithm standard deviation parameter of logarithm normal distribution, wherein the equal step-length of adjacent logarithm standard deviation parameter is d2, according to right
The step-length of number standard deviation criteria successively calculates the logarithm standard deviation parameter σ 1 of n2 logarithm normal distributionj2, wherein 1≤j2≤
n2；
N=n1 × n2 is taken, to μ 1j1With σ 1j2Carry out the distribution parameter (μ that traversal combination obtains n group candidatej,σj), wherein 1
≤j≤n；
Step 2: traversal service life logarithmic average parameter μjWith logarithm standard deviation parameter σjCombination calculate likelihood value, for
Each candidate parameter combination, includes the data group of m lognormal type unit detection information for one group, is detected according to i-th
Information included in TiThe location mode information F at momentiDetermine its corresponding design factor Wi, not according to m detection data
Disconnected iteration updates likelihood value Lj, at the beginning of iteration, set each candidate parameter and combine corresponding likelihood value initial value as 0, every
In likelihood value after the corresponding iteration of a candidate parameter combination, maximizing, that is, LM, then maximum likelihood value LMIt is corresponding
μMFor the estimated value of logarithmic average parameter, σMFor the estimated value of logarithm standard deviation parameter.
In the above scheme, the specific calculating process that candidate distribution parameter is generated in the step 1 is as follows:
(1) the logarithmic average parameter μ 1 of logarithm normal distribution is determinedj1It is as follows with the specific calculating process of step-length d1:
Wherein, μmaxIndicate the logarithmic average parameter upper limit of logarithm normal distribution, μminIndicate the logarithm of logarithm normal distribution
Mean Parameters lower limit, n1 are positive integer, and n1 >=2；
(2) the logarithm standard deviation parameter σ 1 of logarithm normal distribution is determinedj2It is as follows with the specific calculating process of step-length d2:
Wherein, σmaxIndicate the logarithm standard deviation parameter upper limit of logarithm normal distribution, σminIndicate pair of logarithm normal distribution
Number standard deviation criteria lower limits, n2 is positive integer, and n2 >=2；
(3)μ1j1With σ 1j2Traverse combined calculation are as follows:
Enable j=1；J1=1:n1 is traversed in first layer circulation, is traversed j2=1:n2 in second layer circulation, is enabled μj=μ 1j1,
σj=σ 1j2, j=j+1；Wherein, μmax≥μ1j1≥μmin, σmax≥σ1j2≥σmin。
In the above scheme, in the step 2, W is calculatediWith likelihood value LjCalculation formula it is as follows:
Wherein, WiFor design factor, log (*) is natural logrithm function, LjFor likelihood value, μjFor pair of logarithm normal distribution
Number Mean Parameters, σjFor the logarithm standard deviation parameter of logarithm normal distribution.
In the above scheme, likelihood value L in described rapid twojTraversal calculating process it is as follows:
(1) j=1 is enabled；
(2) i=1, L are enabledj=0；
(3) design factor
Wherein, log (*) is natural logrithm function, μjFor the Mean Parameters of logarithm normal distribution, σjFor logarithm normal distribution
Logarithm standard deviation parameter, μjFor the logarithmic average parameter of logarithm normal distribution, LjFor likelihood value, TiFor the inspection of i-th of product
Survey the moment；
(4) i=i+1 is updated, turns (3) if i≤m, otherwise turns (5)；
(5) j=j+1 is enabled, turns (2) if j≤n, otherwise (6)；
(6) in LjMaximizing in (1≤j≤n) remembers it for LM, then μMFor the estimated value of logarithmic average parameter, σMFor
The estimated value of logarithm standard deviation parameter.
Compared with prior art, the beneficial effects of the present invention are: utilizing " a small amount of reliability test data+grind in product
The mass data that stages generate such as make, produce, using ", it estimates the regularity of distribution of life of product, avoids carrying out for product big
The consumption of human and material resources caused by the reliability test of amount and financial resources.
Specific embodiment
Below in conjunction with the case of certain lognormal type unit, the present invention is described in further detail.
A kind of method for estimating lognormal type unit dependability parameter of the present invention, comprising the following steps:
Step 1: candidate service life distribution parameter is determined, according to the distribution of existing lognormal type unit reliability data
Rule primarily determines the logarithmic average parameter lower limit value μ of logarithm normal distribution unit to be estimatedminWith logarithmic average parameter upper limit value
μmaxAnd the logarithm standard deviation parameter lower limit value σ of logarithm normal distribution to be estimatedminWith logarithm standard deviation parameter upper limit value σmax；
In the logarithmic average parameter section of determining logarithm normal distribution unit, n1 candidate logarithm is generated at equal intervals
The logarithmic average parameter of normal distribution, in candidate parameter, the equal step-length of adjacent logarithmic average parameter is d1, equal according to logarithm
The step-length of value parameter successively calculates the logarithmic average parameter μ 1 of n1 logarithm normal distributionj1, wherein 1≤j1≤n1；
In the logarithm standard deviation parameter section of determining logarithm normal distribution unit, it is right that n2 candidate is generated at equal intervals
The logarithm standard deviation parameter of number normal distribution, wherein the equal step-length of adjacent logarithm standard deviation parameter is d2, according to logarithm mark
The step-length of quasi- difference parameter successively calculates the logarithm standard deviation parameter σ 1 of n2 logarithm normal distributionj2, wherein 1≤j2≤n2；
N=n1 × n2 is taken, to μ 1j1With σ 1j2Carry out the distribution parameter (μ that traversal combination obtains n group candidatej,σj), wherein 1
≤j≤n；
Wherein, the logarithmic average parameter μ 1 of logarithm normal distributionj1It is as follows with the specific calculating process of step-length d1:
In formula, μmaxIndicate the logarithmic average parameter upper limit of logarithm normal distribution, μminIndicate the logarithm of logarithm normal distribution
Mean Parameters lower limit, n1 are positive integer, and n1 >=2；
Wherein, the logarithm standard deviation parameter σ 1 of logarithm normal distributionj2It is as follows with the specific calculating process of step-length d2:
In formula, σmaxIndicate the logarithm standard deviation parameter upper limit of logarithm normal distribution, σminIndicate pair of logarithm normal distribution
Number standard deviation criteria lower limits, n2 is positive integer, and n2 >=2；
Wherein, 1 μj1With σ 1j2It is as follows to carry out the combined calculation of traversal:
Enable j=1；J1=1:n1 is traversed in first layer circulation, is traversed j2=1:n2 in second layer circulation, is enabled μj=μ 1j1,
σj=σ 1j2, j=j+1；In formula, μmax≥μ1j1≥μmin, σmax≥σ1j2≥σmin。
Step 2: traversal logarithmic average parameter μjWith logarithm standard deviation parameter σjCombination calculate likelihood value, for each
Candidate parameter combination includes the data group of m lognormal type unit detection information for one group, according to i-th of detection information
Included in TiThe location mode information F at momentiDetermine its corresponding design factor Wi, constantly change according to m detection data
In generation, updates likelihood value Lj, at the beginning of iteration, set each candidate parameter and combine corresponding likelihood value initial value as 0, in each time
It selects in the likelihood value after iteration corresponding to parameter combination, maximizing is denoted as LM, then maximum likelihood value LMIt is corresponding
μMFor the estimated value of logarithmic average parameter, σMFor the estimated value of logarithm standard deviation parameter.
Wherein, design factor Wi, likelihood value LjCalculating and likelihood value LjCalculation formula it is as follows:
In formula, log (*) is natural logrithm function, μjFor the Mean Parameters of logarithm normal distribution, σjFor logarithm normal distribution
Logarithm standard deviation parameter, LjFor likelihood value, TiFor the detection moment of i-th of product；
Wherein, likelihood value L in step 2jTraversal calculating process it is as follows:
(1) j=1 is enabled；
(2) i=1, L are enabledj=0；
(3) design factor
(4) i=i+1 is updated, turns (3) if i≤m, otherwise turns (5)；
(5) j=j+1 is enabled, turns (2) if j≤n, otherwise (6)；
(6) in LjMaximizing in (1≤j≤n) remembers it for LM, then μMFor the estimated value of logarithmic average parameter, σMFor
The estimated value of logarithm standard deviation parameter.
Its logarithmic average ginseng is estimated in embodiment, [F T] the type reliability data such as following table of certain lognormal type unit, examination
Several and logarithm standard deviation parameter.
It is learnt from previous experiences, the logarithmic average parameter of the lognormal type unit is in 3.0~6.0 ranges, with 0.5
For step-length；Logarithm standard deviation parameter is step-length with 0.3, symbiosis is at 56 candidate distribution parameters in 1.0~3.1 ranges
(μj,σj), 1≤j≤56, calculated result is as follows:
As can be seen from the table, in LjMaximum value in (1≤j≤56) is L27, then μ27=4.5, σ27=1.6 is right for this
The estimated value of number Normal Type cell life distribution parameter.
For the feasibility for further verifying the method for the present invention, following simulation model is established.
(1) k1 random number simT is generatedi(1≤i≤k1), simTiObey logarithm normal distribution LN (μ, σ2), it is used for mould
The life value of quasi-simple member.Enable Fi=0, Ti=simTiObtain k1 group [Fi Ti],1≤i≤k1。
(2) k2 random number simT is generatedi(k1+1≤i≤k1+k2), simTiObey logarithm normal distribution LN (μ, σ2),
Life value for analogue unit.
(3) k2 uniform random number simTc is generatedi(k1+1≤i≤k1+k2) is used for the mock survey moment.
(4) it within the scope of k1+1≤i≤k1+k2, enables
Using emulating obtained k1+k2 group lifetime data [F abovei Ti] after, distribution ginseng can be obtained by reapplying context of methods
Several estimated values.With μ=4.5, σ=1.6, k1=5, for k2=15, the logarithm that is obtained after a large amount of emulation with context of methods
The mean value of Normal Type unit logarithmic average parametric statistics result is 4.46, root variance is 0.54, logarithm standard deviation parametric statistics knot
The mean value of fruit is 1.50, root variance is 0.38.If using k1+k2 group lifetime data simTiIf, using theoretical method meter
The mean value of obtained logarithmic average parametric statistics result is 4.54, root variance is 0.39, logarithm standard deviation parametric statistics result
Mean value be 1.58, root variance is 0.25, the difference of the two is within engineering allowed band.
The above is only embodiments of the present invention, are not intended to limit the scope of the invention, all to utilize the present invention
Equivalent structure or equivalent flow shift made by description is applied directly or indirectly in other correlative technology fields,
It is included within the scope of the present invention.
Claims (4)
1. a kind of method for estimating lognormal type unit dependability parameter, which is characterized in that obey lognormal for the service life
The unit of distribution carries out dependability parameter estimation, comprising the following steps:
Step 1: determining candidate service life distribution parameter, according to the regularity of distribution of existing lognormal type unit reliability data,
Primarily determine the service life logarithmic average parameter lower limit value μ of logarithm normal distribution unit to be estimatedminWith logarithmic average parameter upper limit value
μmaxAnd the logarithm standard deviation parameter lower limit value σ of logarithm normal distribution to be estimatedminWith logarithm standard deviation parameter upper limit value σmax；
In the service life logarithmic average parameter section of determining logarithm normal distribution unit, n1 candidate logarithm is being generated at equal intervals just
The logarithmic average parameter of state distribution, in candidate parameter, the equal step-length of adjacent logarithmic average parameter is d1, is joined according to logarithmic average
Several step-lengths successively calculates the logarithmic average parameter μ 1 of n1 logarithm normal distributionj1, wherein 1≤j1≤n1；
In the service life logarithm standard deviation parameter section of determining logarithm normal distribution unit, n2 candidate logarithm is generated at equal intervals
The logarithm standard deviation parameter of normal distribution, wherein the equal step-length of adjacent logarithm standard deviation parameter is d2, according to logarithm standard deviation
The step-length of parameter successively calculates the logarithm standard deviation parameter σ 1 of n2 logarithm normal distributionj2, wherein 1≤j2≤n2；
N=n1 × n2 is taken, to μ 1j1With σ 1j2Carry out the distribution parameter (μ that traversal combination obtains n group candidatej, σj), wherein 1≤j≤
n；
Step 2: traversal service life logarithmic average parameter μjWith logarithm standard deviation parameter σjCombination calculate likelihood value, for each time
Parameter combination is selected, includes the data group of m lognormal type unit detection information for one group, according to i-th of detection information institute
Include in TiThe location mode information F at momentiDetermine its corresponding design factor Wi, more according to the continuous iteration of m detection data
New likelihood value Lj, at the beginning of iteration, set each candidate parameter and combine corresponding likelihood value initial value as 0, in each candidate parameter
In likelihood value after the corresponding iteration of combination, maximizing, that is, LM, then maximum likelihood value LMCorresponding μMIt is equal for logarithm
The estimated value of value parameter, σMFor the estimated value of logarithm standard deviation parameter.
2. the method for lognormal type unit dependability parameter according to claim 1, it is characterised in that: the step 1
The middle specific calculating process for generating candidate distribution parameter is as follows:
(1) the logarithmic average parameter μ 1 of logarithm normal distribution is determinedj1It is as follows with the specific calculating process of step-length d1:
Wherein, μmaxIndicate the logarithmic average parameter upper limit of logarithm normal distribution, μminIndicate the logarithmic average of logarithm normal distribution
Parameter lower limit, n1 are positive integer, and n1 >=2；
(2) the logarithm standard deviation parameter σ 1 of logarithm normal distribution is determinedj2It is as follows with the specific calculating process of step-length d2:
Wherein, σmaxIndicate the logarithm standard deviation parameter upper limit of logarithm normal distribution, σminIndicate the logarithm mark of logarithm normal distribution
Quasi- difference parameter lower limit, n2 are positive integer, and n2 >=2；
(3)μ1j1With σ 1j2Traverse combined calculation are as follows:
Enable j=1；J1=1: n1 is traversed in first layer circulation, is traversed j2=1: n2 in second layer circulation, is enabled μj=μ 1j1, σj=σ
1j2, j=j+1；Wherein, μmax≥μ1j1≥μmin, σmax≥σ1j2≥σmin。
3. the method for lognormal type unit dependability parameter according to claim 1, it is characterised in that: the step 2
Middle calculating WiWith likelihood value LjCalculation formula it is as follows:
Wherein, WiFor design factor, log (*) is natural logrithm function, σjFor the logarithm standard deviation parameter of logarithm normal distribution, μj
For the logarithmic average parameter of logarithm normal distribution.
4. a kind of method for estimating lognormal type unit dependability parameter according to claim 1 or 3, feature exist
In: likelihood value L in the step 2jTraversal calculating process it is as follows:
(1) j=1 is enabled；
(2) i=1, L are enabledj=0；
(3) design factor
Wherein, μjFor the Mean Parameters of logarithm normal distribution, σjFor the logarithm standard deviation parameter of logarithm normal distribution, μjFor logarithm
The logarithmic average parameter of normal distribution, LjFor likelihood value, TiFor the detection moment of i-th of product；
(4) i=i+1 is updated, turns (3) if i≤m, otherwise turns (5)；
(5) j=j+1 is enabled, turns (2) if j≤n, otherwise (6)；
(6) in LjMaximizing in (1≤j≤n) remembers it for LM, then μMFor the estimated value of logarithmic average parameter, σMFor logarithm mark
The estimated value of quasi- difference parameter.
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